document.write( "Question 581429: Would someone please help me with this problem with step by step instructions?\r
\n" ); document.write( "\n" ); document.write( "Solve the systems of equations by graphing
\n" ); document.write( "5x + y = 18
\n" ); document.write( "6x + 7y = -19
\n" ); document.write( "What is the solution? Is it consistent or inconsistent?
\n" ); document.write( "Dependent or independent?
\n" ); document.write( "(I do not know what that means) \n" ); document.write( "

Algebra.Com's Answer #371775 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
5x + y = 18
\n" ); document.write( "6x + 7y = -19
\n" ); document.write( "to graph this we want the equations in the slope intercept form; y = mx + b
\n" ); document.write( "We will graph each equation separately, then together
\n" ); document.write( "y = -5x + 18
\n" ); document.write( "We need at least two points to graph a linear equation, substitute for x and find y, A table
\n" ); document.write( ":
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( "-2 |28; (y = -5(-2) + 18; y = +10 + 18)
\n" ); document.write( " 0 |18
\n" ); document.write( "+2 | 8
\n" ); document.write( ":
\n" ); document.write( "The graph looks like this
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-20%2C+30%2C+-5x%2B18%29+\"$
\n" ); document.write( ":
\n" ); document.write( "Do the same with the 2nd equation
\n" ); document.write( "6x +7y = -19
\n" ); document.write( "7y = -6x - 19
\n" ); document.write( "y = $\"-6%2F7\"$ x - $\"19%2F7\"$
\n" ); document.write( ":
\n" ); document.write( "x | y
\n" ); document.write( "-------
\n" ); document.write( "-2 |-1;
\n" ); document.write( " 0 |-19
\n" ); document.write( "+5 |-7
\n" ); document.write( ":
\n" ); document.write( "The graph looks like this
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-20%2C+30%2C+%28-6%2F7%29x-%2819%2F7%29%29+\"$
\n" ); document.write( ":
\n" ); document.write( "Together:
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-20%2C+30%2C+-5x%2B18%2C+%28-6%2F7%29x-%2819%2F7%29%29+\"$
\n" ); document.write( "Where the two graphs intersect x=5, y=-7 is the solution to this system
\n" ); document.write( "And it is the only solutions so it \"consistent\"
\n" ); document.write( "and
\n" ); document.write( "in this system x = the independent variable and y is the dependent
\n" ); document.write( ":
\n" ); document.write( "Another words the value of y is dependent on the value of x
\n" ); document.write( ";
\n" ); document.write( "Note that you can confirm this if you substitute 5 for x and -7 for y in both original equations, you find the equations are true, for this solution \n" ); document.write( "

\n" );